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Uniformity in all orientations
In physics and geometry, isotropy (from Ancient Greek ἴσος (ísos) 'equal' and τρόπος (trópos) 'turn, way') is uniformity in all orientations. Precise definitions
Isotropy
Linear representation of a group on the tangent space to a fixed point of the group
In differential geometry, the isotropy representation is a natural linear representation of a Lie group, that is acting on a manifold, on the tangent space
Isotropy_representation
Geological concept
properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse plane has infinite planes of symmetry and thus, within
Transverse_isotropy
2024 EP by Onewe
Planet Nine: Isotropy is the third extended play by the South Korean band Onewe. It was released by RBW and distributed by Kakao Entertainment on April
Planet_Nine:_Isotropy
Transformations induced by a mathematical group
{\displaystyle G} with respect to x {\displaystyle x} (also called the isotropy group or little group) is the set of all elements in G {\displaystyle G}
Group_action
Theory that the universe is the same in all directions
structural consequences of the cosmological principle are homogeneity and isotropy. Homogeneity – constant density – means that the same observational evidence
Cosmological_principle
Concept in relativity theory
special relativity. However, those experiments cannot directly establish the isotropy of the one-way speed of light since it has been shown that slow clock-transport
One-way_speed_of_light
Quadratic form for which there is a non-zero vector on which the form evaluates to zero
subspace if it does not contain any (non-zero) isotropic vectors. The isotropy index of a quadratic space is the maximum of the dimensions of the totally
Isotropic_quadratic_form
Object or material which allows the flow of electric charge with little energy loss
In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions
Electrical_conductor
differentiable manifold M. An isotropy group is the subgroup of G fixing a chosen point of M. An isotropy type is a conjugacy class of isotropy groups. The principal
Principal_orbit_type_theorem
In geometry, property of being directionally dependent
structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according
Anisotropy
Solid material whose physical properties are independent of orientation
the finite sizes of atoms and bonding considerations ensure that true isotropy of atomic position will not exist in the solid state, it is possible for
Isotropic_solid
comparison-, clock anisotropy-, mass isotropy-, or energy isotropy experiments) are spectroscopic tests of the isotropy of mass and space. Although originally
Hughes–Drever_experiment
Mathematical model of the Big Bang
metric, assumes that the universe looks the same in all directions (isotropy) and from every location (homogeneity) on a large enough scale: "the universe
Lambda-CDM_model
Metric based on the exact solution of Einstein's field equations of general relativity
of the metric follows from the geometric properties of homogeneity and isotropy. Depending on geographical or historical preferences, the set of the four
Friedmann–Lemaître–Robertson–Walker metric
Friedmann–Lemaître–Robertson–Walker_metric
J^{-1}{\boldsymbol {F}}^{-T}{\boldsymbol {M}}{\boldsymbol {F}}^{T}} (non isotropy) τ = {\displaystyle {\boldsymbol {\tau }}=\,} J σ {\displaystyle J{\boldsymbol
Alternative_stress_measures
Contraction of length in the direction of propagation in Minkowski space
play the same role in Minkowski geometry (the Lorentz group forms the isotropy group of the self-isometries of the spacetime) which are played by rotations
Length_contraction
Speed of electromagnetic waves
the motion of the Earth with respect to this medium, by measuring the isotropy of the speed of light. Beginning in the 1880s several experiments were
Speed_of_light
Mathematical concept in differential geometry
Euclidean spaces, polar actions are called polar representations. The isotropy representations of Riemannian symmetric spaces are basic examples of polar
Polar_action
Physical theory of the cosmos
separation of any two regions of space that are in causal contact. The observed isotropy of the CMB is problematic in this regard: if the universe had been dominated
Big_Bang
Cylindrical conformal map projection
The Mercator projection is conformal. One implication of that is the "isotropy of scale factors", which means that the point scale factor is independent
Mercator_projection
Hypothetical field that may have driven cosmic inflation
which consequently forms a universe consistent with observed spatial isotropy and homogeneity. The basic[clarification needed] model of inflation proceeds
Inflaton
Everything in space and time
general relativity and on symmetry assumptions such as the homogeneity and isotropy of space. A version of the model with a cosmological constant (Lambda)
Universe
Trace radiation from the early universe
origin. In the 1970s numerous studies showed that tiny deviations from isotropy in the CMB could result from events in the early universe. Harrison, Peebles
Cosmic_microwave_background
1887 investigation of the speed of light
is generally considered the solution to all negative aether drift (or isotropy of the speed of light) measurements, including the Michelson–Morley null
Michelson–Morley_experiment
entropic, entropion, entropy, heliotropism, isentropic, isotrope, isotropic, isotropy, pleiotropic, pleiotropy, polytrope, protrepsis, protreptic, psychotropic
List of Greek and Latin roots in English/P–Z
List_of_Greek_and_Latin_roots_in_English/P–Z
Generalized manifold
discontinuous action of a possibly infinite group of diffeomorphisms with finite isotropy subgroups. In particular this applies to any action of a finite group;
Orbifold
Measure of material deformation perpendicular to loading
materials have a plane of isotropy in which the elastic properties are isotropic. If we assume that this plane of isotropy is the yz-plane, then Hooke's
Poisson's_ratio
Uniformity of a material or system at every point
compacted. However, homogeneity of materials does not necessarily mean isotropy. In the previous example, a composite material may not be isotropic. In
Homogeneity_(physics)
anisotropy, both of them are called transverse isotropy (it is called transverse isotropy because there is isotropy in either the horizontal or vertical plane)
Seismic_anisotropy
Measurement of distance
the sky systematically blue-shifted or red-shifted. Thus, isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special
Comoving_and_proper_distances
Experiments probing the accuracy of special relativity's predictions
be interpreted in different ways when viewed individually. For example, isotropy experiments such as Michelson-Morley can be seen as a simple consequence
Tests_of_special_relativity
Theory of forces and subatomic particles
predominance of matter over antimatter (matter/antimatter asymmetry). The isotropy and homogeneity of the visible universe over large distances seems to require
Standard_Model
Integral transform type in mathematics
X = G/H, a generalized sphere centered at a point x0 is an orbit of the isotropy group of x0. The model case for orbital integrals is a Riemannian symmetric
Orbital_integral
South Korean band
March 27, Onewe announced their return with their third EP Planet Nine: Isotropy, to be released on April 17, 2024. To commemorate the release of the new
Onewe
1938 experiment confirming relativistic time dilation
In physics, the Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light. The result was in agreement
Ives–Stilwell_experiment
Idealized physical body that absorbs all incident electromagnetic radiation
spectrum at a temperature of about 2.7 K. It departs from the perfect isotropy of true black-body radiation by an observed anisotropy that varies with
Black_body
Structures in rock caused by extension
ribbon-like boudins or chocolate-tablet boudins, depending on the axis and isotropy of extension. They range in size from about 20 m thick to about 1 cm. There
Boudinage
Use of mathematical models to simulate turbulent flow
accuracy. Eddy viscosity based closures cannot account for the return to isotropy of turbulence, observed in decaying turbulent flows. Eddy-viscosity based
Turbulence_modeling
a Fluid Universe". Scientific American. Retrieved 2015-12-22. Testing gaussianity, homogeneity and isotropy with the cosmic microwave background v t e
Non-Gaussianity
Region in space
R.; et al. (Planck Collaboration) (2013). "Planck 2013 results. XXIII. Isotropy and statistics of the CMB". Astronomy & Astrophysics. 571: A23. arXiv:1303
CMB_cold_spot
Principle that humans are not privileged observers of the universe
evidence from galaxy clusters, quasars, and type Ia supernovae suggests that isotropy is violated on large scales. Furthermore, various large-scale structures
Copernican_principle
Construction for n-dimensional noise functions
the patent claims, which expired on January 8, 2022. OpenSimplex noise Isotropy Ken Perlin, Noise hardware. In Real-Time Shading SIGGRAPH Course Notes
Simplex_noise
Theorem in physical cosmology
generalized to an arbitrary space-time with no appeal to homogeneity or isotropy. The Friedmann–Lemaître–Robertson–Walker metric is given by d s = d t 2
Borde–Guth–Vilenkin_theorem
Time reversal symmetry in physics
entropy? This view, supported by cosmological observations (such as the isotropy of the cosmic microwave background) connects this problem to the question
T-symmetry
Physical field surrounding an electric charge
proportional. Materials can have varying extents of linearity, homogeneity and isotropy. The invariance of the form of Maxwell's equations under Lorentz transformation
Electric_field
Refractive property of materials
(i.e., stretched or bent) causing a loss of physical isotropy and consequently a loss of isotropy in the material's permittivity tensor; Form birefringence
Birefringence
Representation of a quantum mechanical system
number of modulus 1, this gives the U(1) factor of the isotropy group. The other part of the isotropy group is parametrized by the unitary matrices on the
Bloch_sphere
Theory of interwoven space and time by Albert Einstein
explicit postulates, but also on several tacit assumptions, including the isotropy and homogeneity of space and the independence of measuring rods and clocks
Special_relativity
Type of metamorphic rock
preference has to do with its softness, which made it easier to carve, relative isotropy and homogeneity, and a relative resistance to shattering. Also, the low
Marble
Notion for convergence of metric spaces
04800 [cs.RO]. Sormani, Christina (2004). "Friedmann cosmology and almost isotropy". Geometric and Functional Analysis. 14 (4). arXiv:math/0302244. doi:10
Gromov–Hausdorff_convergence
Mathematical group
an isomorphism of k v {\displaystyle k_{v}} -algebras. If we take the isotropy subgroup of G {\displaystyle G} for the valuation class w {\displaystyle
Galois_group
Manifold with inversion symmetry
In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure.
Hermitian_symmetric_space
British X-ray astronomer
2011, at the Wayback Machine Fabian, Andrew Christopher. The small-scale isotropy of the cosmic X-ray background. mssl.ucl.ac.uk (PhD thesis). University
Andrew_Fabian
Mathematical structure in differential geometry
authors. The isotropy Lie algebra of a Poisson manifold ( M , π ) {\displaystyle (M,\pi )} at a point x ∈ M {\displaystyle x\in M} is the isotropy Lie algebra
Poisson_manifold
Form of matter
and the arrangement of the cellular structure (open vs closed and pore isotropy).[citation needed] To characterize the mechanical properties of foams,
Foam
groups appearing, the lists present the Lie algebra of the isotropy group rather than the isotropy group itself. Here Λ3 0C6 ≅ C14 denotes the space of 3-forms
Prehomogeneous_vector_space
Family of linear transformations
observers in different inertial frames, as is shown using homogeneity and isotropy of space. The transformation sought after thus must possess the property
Lorentz_transformation
Technique in microfabrication used to remove material and create structures
material. A highly selective etch leaves the underlying material unharmed. Isotropy Red: masking layer; yellow: layer to be removed A perfectly isotropic etch
Etching_(microfabrication)
Mathematical description of spacetime used in relativity
postulate of special relativity, together with homogeneity of spacetime and isotropy of space, it follows that the spacetime interval between two arbitrary
Minkowski_spacetime
Theory of rapid universe expansion
made the Universe more chaotic, could lead to statistical homogeneity and isotropy. In 1965, Erast Gliner showed that the simplest energy-momentum tensor
Cosmic_inflation
Hypothesis in physics
order to account for the presently observed almost spatial homogeneity and isotropy of our universe. Gravitational singularity Unsolved problems in physics
Weyl_curvature_hypothesis
Branch of mathematics
isolated quotient singularities. In particular, if these singularities have isotropy groups G i {\displaystyle G_{i}} then the map K 0 ( X ) → K 0 ( X ) {\displaystyle
K-theory
Space observatory
respect to viewing angle in the sky, determining that "deviations from isotropy have been found and demonstrated to be robust against component separation
Planck_(spacecraft)
Mathematical invariance under transformations
Fixed points of isometry groups in Euclidean space – center of symmetry Isotropy Palindrome Spacetime symmetries Spontaneous symmetry breaking Symmetry-breaking
Symmetry
Vector field describing the density of electric dipole moments in a dielectric material
although more generally it is a tensor. This is a particular case due to the isotropy of the dielectric. Taking into account this relation between P and E, equation
Polarization_density
1991 astronomical survey
document the so-called "end of greatness" where the Cosmological Principle of isotropy could be seen. Superclusters and voids are prominent features in the survey
Las_Campanas_Redshift_Survey
Category where every morphism is invertible; generalization of a group
which is just the isotropy subgroup at x {\displaystyle x} for the given action (which is why vertex groups are also called isotropy groups). Similarly
Groupoid
Mathematical model of turbulence
one- and two-equation based closures cannot account for the return to isotropy of turbulence, observed in decaying turbulent flows. Eddy-viscosity based
Reynolds stress equation model
Reynolds_stress_equation_model
Metamaterial that uses surface plasmons to achieve optical properties not seen in nature
create a three-dimensional array of split-ring resonators that exhibits isotropy when rotated in any direction up to an incident angle of 40 degrees. Exposing
Plasmonic_metamaterial
Hypothetical Solar System planet
Retrieved 25 April 2020. Bernardelli, Pedro; et al. (2020). "Testing the isotropy of the Dark Energy Survey's extreme trans-Neptunian objects". The Planetary
Planet_Nine
Mean kinetic energy per unit mass of eddies in turbulent flow
depends upon the turbulence model used; k–ε (k–epsilon) models assume isotropy of turbulence whereby the normal stresses are equal: ( u ′ ) 2 ¯ = ( v
Turbulence_kinetic_energy
Internal groupoid in the category of smooth manifolds
diffeomorphism; the unit map u {\displaystyle u} is a smooth embedding; the isotropy groups G x {\displaystyle G_{x}} are Lie groups; the orbits O x ⊆ M {\displaystyle
Lie_groupoid
difference in behavior is due ultimately to the fact that spacetimes have isotropy subgroups which are subgroups of the Lorentz group SO+(1,3), which is a
Cartan–Karlhede_algorithm
Any of certain special normal subgroups of a group
the isotropy subgroup of any point acts as the identity on its entire orbit. Thus, in case the action is transitive, the normal core of any isotropy subgroup
Core_(group_theory)
Mathematical solution in general relativity
any adapted observer. From this expression, it is easy to see that the isotropy group of our non-null electrovacuum is generated by boosts in the e → 3
Electrovacuum_solution
Belarusian academic and mass shooter (1940–2026)
advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling. Mathieu Beauregard, La folie de Valery Fabrikant:
Valery_Fabrikant
Equations in physical cosmology
papers in the 1922-1923 time frame. He adopted the same homogeneity and isotropy assumptions used by Albert Einstein and by Willem de Sitter in their papers
Friedmann_equations
(pseudo-)Riemannian manifold whose geodesics are reversible
is a symmetric space G / K with a compact isotropy group K. Conversely, symmetric spaces with compact isotropy group are Riemannian symmetric spaces, although
Symmetric_space
Atmospheric effect caused by the solar wind
source region of discrete auroras inferred from their relationship with isotropy boundaries of energetic particles". Annales Geophysicae. 15 (8): 943. Bibcode:1997AnGeo
Aurora
State of matter
conditions, the diffraction pattern has circular symmetry, expressing the isotropy of the liquid. Radially, the diffraction intensity smoothly oscillates
Liquid
Mathematical model of how solid objects deform
\\0&0&0&0&0&C_{66}\end{bmatrix}}.} When the transverse isotropy is weak (i.e. close to isotropy), an alternative parametrization utilizing Thomsen parameters
Linear_elasticity
Pattern of birefringence colors
dark bands correspond to positions where optical extinction (apparent isotropy) would be seen. In other words, the interference figure presents all possible
Conoscopic interference pattern
Conoscopic_interference_pattern
Electrically insulating substance able to be polarised by an applied electric field
rate? Does the response depend on the direction of the applied field (isotropy of the material)? Is the response the same everywhere (homogeneity of the
Dielectric
State of matter with properties of both conventional liquids and crystals
Yamamoto J, Nishiyama I, Inoue M, Yokoyama H (September 2005). "Optical isotropy and iridescence in a smectic 'blue phase'". Nature. 437 (7058): 525–8.
Liquid_crystal
Property of a planar object which maps onto itself after rotation by any angle
depending on the distance to the origin only, such as a central force. Isotropy Rotational symmetry Particle in a spherically symmetric potential Gauss's
Circular_symmetry
Anomaly in cosmic microwave background
2010-02-07. Planck Collaboration (2013). "Planck 2013 results. XXIII. Isotropy and statistics of the CMB". Astronomy & Astrophysics. 571 (27): A23. arXiv:1303
Axis_of_evil_(cosmology)
and isotropy group SO(1,1) x SO(2), null electrovacuums and null dusts have Segre type { ( 2 , 11 ) } {\displaystyle \{\,(2,11)\}} and isotropy group
Exact solutions in general relativity
Exact_solutions_in_general_relativity
American theoretical physicist (1927–2012)
quasar group, since general relativity does not presuppose homogeneity or isotropy, i.e. the cosmological principle. Sachs believed that fundamental incompatibilities
Mendel_Sachs
Non-Euclidean geometry
that space is continuous, homogeneous, isotropic, and without boundaries. Isotropy is guaranteed by the fourth postulate, that all right angles are equal
Elliptic_geometry
American physicist (1933–2024)
on January 22, 2024, at age 90. Wilson, R. W.; Penzias, A. A. (1967). "Isotropy of Cosmic Background Radiation at 4080 Megahertz". Science. 156 (3778):
Arno_Allan_Penzias
Statistical model
defined through the covariance function are the process' stationarity, isotropy, smoothness and periodicity. Stationarity refers to the process' behaviour
Gaussian_process
Cosmological solution to the Einstein field equations of general relativity
q=-1} ), thus satisfying the perfect cosmological principle that assumes isotropy and homogeneity throughout space and time. There are ways to cast de Sitter
De_Sitter_universe
Microstructure of natural materials
especially its fracture resistance, and enables strength and in plane isotropy. It is found in various natural structures, including the cosmoid scale
Bouligand_structure
Topics referred to by the same term
Invincible (comics) and its TV adaptation Invincible (TV series) Isotone Isotropy, an unrelated concept Isotype (disambiguation) iZotope, Inc., an audio
Isotope_(disambiguation)
Non-commutative group with 6 elements
every x in X, we define the stabilizer subgroup of x (also called the isotropy group or little group) as the set of all elements in G that fix x: G x
Dihedral_group_of_order_6
Non-standard model of the universe; emphasizes the role of ionized gases
writing that "there is no way that the results can be consistent with the isotropy of the cosmic microwave background radiation and X-ray backgrounds". In
Plasma_cosmology
Borrill et al. SIToolBox — SI Toolbox is a package for estimating the isotropy violation in the CMB sky. It is developed by Das et al. and it consists
List of cosmological computation software
List_of_cosmological_computation_software
redshift and distance derives from the general assumption of uniformity and isotropy rather than specifically from general relativity. However the prediction
Tests_of_general_relativity
Method of smoothing using a spline function
when smoothing with respect to spatial location, but in many other cases isotropy is not an appropriate assumption and can lead to sensitivity to apparently
Smoothing_spline
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